EXAMPLE 4 Solve a multi-step problem

Computers

You are buying a new computer and find 10 models in a store advertisement. The prices are $890, $750, $650, $370, $660, $670, $450, $650, $725, and $825.

Find the mean of the computer prices.

You are willing to pay the mean price with an absolute deviation of at most $100. How many of the computer prices meet your condition?

EXAMPLE 4 Solve a multi-step problem

SOLUTION

STEP 1

Find the mean by dividing the sum of the prices by 10.

=664010 = 664

Mean =890 + 750 + 650 + 370 + 660 + 670 + 450 + 650 + 725 + 825

10

EXAMPLE 4 Solve a multi-step problem

STEP 2

Write and solve an inequality. An absolute deviation of at most $100 from the mean, $664, is given by the inequality x – 664 ≤ 100.

Write absolute value inequality.x – 664 ≤ 100

– 100 ≤ x – 664 ≤ 100 Write as compound inequality.

564 ≤ x ≤ 764 Add 664 to each expression.

EXAMPLE 4 Solve a multi-step problem

ANSWER

The prices you will consider must be at least $564 and at most $764. Six prices meet your condition: $750, $650, $660, $670, $650, and $725.

GUIDED PRACTICE for Example 4

7. WHAT IF? In Example 4, suppose that you are willing to pay the mean price with an absolute

deviation of at most $75. How many of the computer prices meet this condition?

ANSWER

5 computer prices